Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists, and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains expository articles by program participants describing the present state of the art. Here researchers and graduate students will encounter Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.
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Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists, and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains expository articles by program participants describing the present state of the art. Here researchers and graduate students will encounter Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.
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ABSTRACT. This article traces several prominent trends in the development of the subject of holomorphic spaces, with emphasis on operator-theoretic aspects. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
regular factorizations, commuting nonselfadjoint operators, tight uniform algebras, complete characteristic function, unconditionally converging operator, unitary colligation, output determinantal representations, superoptimal approximation, bounded point evaluations, scalar characteristic function, abstract interpolation problem, cellular indecomposable, robust stabilisation problem, cyclic subnormal operators, minimal unitary dilation, minimal unitary extension, functional embeddings, tight subspace, commutant lifting theorem, completely nonunitary contraction, algebraic scattering systems, distinguished homomorphism, holomorphic spaces, symplectic plane, invariant subspace structure Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Theory Adv, Integral Equations Operator Theory, Acta Math, Academic Press, Reine Angew, Publications Volume, London Math, Michigan Math, Indiana Univ, Duke Math, Schatten-von Neumann, Regional Conference Series, Soviet Math, Cambridge Univ, Functional Anal, Harry Dym, Mathematical Sciences Research Institute, Petersburg Math, Acta Sci, American Mathematical Society, Analyse Math, Englewood Cliffs, Leningrad Math, Research Notes New!
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ABSTRACT. This article traces several prominent trends in the development of the subject of holomorphic spaces, with emphasis on operator-theoretic aspects. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
regular factorizations, commuting nonselfadjoint operators, tight uniform algebras, complete characteristic function, unconditionally converging operator, unitary colligation, output determinantal representations, superoptimal approximation, bounded point evaluations, scalar characteristic function, abstract interpolation problem, cellular indecomposable, robust stabilisation problem, cyclic subnormal operators, minimal unitary dilation, minimal unitary extension, functional embeddings, tight subspace, commutant lifting theorem, completely nonunitary contraction, algebraic scattering systems, distinguished homomorphism, holomorphic spaces, symplectic plane, invariant subspace structure Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Theory Adv, Integral Equations Operator Theory, Acta Math, Academic Press, Reine Angew, Publications Volume, London Math, Michigan Math, Indiana Univ, Duke Math, Schatten-von Neumann, Regional Conference Series, Soviet Math, Cambridge Univ, Functional Anal, Harry Dym, Mathematical Sciences Research Institute, Petersburg Math, Acta Sci, American Mathematical Society, Analyse Math, Englewood Cliffs, Leningrad Math, Research Notes New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 31
books:
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20
books
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- Subnormal Operators (Research notes in mathematics) by J.B. Conway on page 201, page 202, and page 204
- Linear Operators, Part 1: General Theory (Pure and Applied Mathematics, Vol. 7) by Nelson Dunford on page 133, and page 153
- Global Analysis on Foliated Spaces (Mathematical Sciences Research Institute Publications) by Calvin C. Moore in Front Matter
- Current Topics in Complex Algebraic Geometry (Mathematical Sciences Research Institute Publications) by Herbert Clemens in Front Matter
- Comparison Geometry (Mathematical Sciences Research Institute Publications) by Karsten Grove in Front Matter
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- Reproducing Kernel Spaces and Applications (Operator Theory: Advances and Applications) by Daniel Alpay on page 211, and page 212
- Global Analysis on Foliated Spaces (Mathematical Sciences Research Institute Publications) by Calvin C. Moore in Front Matter
- A Sampler of Riemann-Finsler Geometry (Mathematical Sciences Research Institute Publications) by David Bao in Front Matter
- Convex Geometric Analysis (Mathematical Sciences Research Institute Publications) by Keith M. Ball in Front Matter
- Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models (Cambridge Studies in Advanced Mathematics) by Fritz Gesztesy in Back Matter
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